Do you see this 20 mv (P-P) hum with input shorted? If so, you power filtering is not adequate. Are you sure that ALL your electrolytic capacitors are functional?

Yes, input is shorted. Right now I use CLC filter 200uF + 4H choke + 100 uF. May be on of the cap is defective, I can't exclude that. I also suspect this might be due to long wires from power supply (it is mounted separately for a while).

But at the moment oscillation at LTP 6N6P is a problem #1.

As Geek from DIYTube.com suggested, 6N6P is prone to oscillation which is very difficult to get rid of. I'm going to buy 12BH7 (original schematic used them), and 6CG7 (very linear triodes). So I will try to use these tubes instead of 6N6P.